Question
Kim went to the store to buy a new TV. The sales clerk asked "How large is your current TV?". Kim replied "It is 25 inches wide and 14 inches tall". The sales clerk explained that TVs are sold by the measurement along the diagonal of the screen. Save Kim a trip home to remeasure - What is the diagonal measurement for Kim's current TV?
Ask by Pierce Moran. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Kim's current TV has a diagonal measurement of approximately 28.7 inches.
Solution
To find the diagonal measurement of Kim's current TV, you can use the Pythagorean theorem, which is applicable since the TV screen forms a right-angled triangle with its width and height.
**Given:**
- **Width (W) = 25 inches**
- **Height (H) = 14 inches**
**Formula:**
\[
\text{Diagonal (D)} = \sqrt{W^2 + H^2}
\]
**Calculation:**
\[
D = \sqrt{25^2 + 14^2} = \sqrt{625 + 196} = \sqrt{821} \approx 28.66 \text{ inches}
\]
**Rounded to one decimal place:**
\[
D \approx 28.7 \text{ inches}
\]
**Conclusion:**
Kim's current TV has a diagonal measurement of approximately **28.7 inches**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find the diagonal measurement of Kim's current TV, we can use the Pythagorean theorem: \( c = \sqrt{a^2 + b^2} \), where \( c \) is the diagonal, and \( a \) and \( b \) are the width and height, respectively. Plugging in Kim's dimensions: \( c = \sqrt{25^2 + 14^2} \) Calculating that, we have: \( c = \sqrt{625 + 196} = \sqrt{821} \approx 28.7 \) inches. So, Kim's TV has a diagonal measurement of approximately 28.7 inches! Now Kim is all set to upgrade without making an unnecessary trip home!
